Solve by Substitution 4x-y=3 , 7x-9y=-2

$4 x - y = 3$ , $7 x - 9 y = - 2$

Solve for $y$ in the first equation.

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Subtract $4 x$ from both sides of the equation.

$- y = 3 - 4 x$

$7 x - 9 y = - 2$

Multiply each term in $- y = 3 - 4 x$ by $- 1$

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Multiply each term in $- y = 3 - 4 x$ by $- 1$ .

$(- y) \cdot - 1 = 3 \cdot - 1 + (- 4 x) \cdot - 1$

$7 x - 9 y = - 2$

Multiply $(- y) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 y = 3 \cdot - 1 + (- 4 x) \cdot - 1$

$7 x - 9 y = - 2$

Multiply $y$ by $1$ .

$y = 3 \cdot - 1 + (- 4 x) \cdot - 1$

$7 x - 9 y = - 2$

$y = 3 \cdot - 1 + (- 4 x) \cdot - 1$

$7 x - 9 y = - 2$

Simplify each term.

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Multiply $3$ by $- 1$ .

$y = - 3 + (- 4 x) \cdot - 1$

$7 x - 9 y = - 2$

Multiply $- 1$ by $- 4$ .

$y = - 3 + 4 x$

$7 x - 9 y = - 2$

$y = - 3 + 4 x$

$7 x - 9 y = - 2$

$y = - 3 + 4 x$

$7 x - 9 y = - 2$

$y = - 3 + 4 x$

$7 x - 9 y = - 2$

Replace all occurrences of $y$ with $- 3 + 4 x$ in each equation.

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Replace all occurrences of $y$ in $7 x - 9 y = - 2$ with $- 3 + 4 x$ .

$7 x - 9 (- 3 + 4 x) = - 2$

$y = - 3 + 4 x$

Simplify $7 x - 9 (- 3 + 4 x)$ .

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Simplify each term.

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Apply the distributive property.

$7 x - 9 \cdot - 3 - 9 (4 x) = - 2$

$y = - 3 + 4 x$

Multiply $- 9$ by $- 3$ .

$7 x + 27 - 9 (4 x) = - 2$

$y = - 3 + 4 x$

Multiply $4$ by $- 9$ .

$7 x + 27 - 36 x = - 2$

$y = - 3 + 4 x$

$7 x + 27 - 36 x = - 2$

$y = - 3 + 4 x$

Subtract $36 x$ from $7 x$ .

$- 29 x + 27 = - 2$

$y = - 3 + 4 x$

$- 29 x + 27 = - 2$

$y = - 3 + 4 x$

$- 29 x + 27 = - 2$

$y = - 3 + 4 x$

Solve for $x$ in the first equation.

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Move all terms not containing $x$ to the right side of the equation.

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Subtract $27$ from both sides of the equation.

$- 29 x = - 2 - 27$

$y = - 3 + 4 x$

Subtract $27$ from $- 2$ .

$- 29 x = - 29$

$y = - 3 + 4 x$

$- 29 x = - 29$

$y = - 3 + 4 x$

Divide each term by $- 29$ and simplify.

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Divide each term in $- 29 x = - 29$ by $- 29$ .

$\frac{- 29 x}{- 29} = \frac{- 29}{- 29}$

$y = - 3 + 4 x$

Cancel the common factor of $- 29$ .

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Cancel the common factor.

$\frac{- 29 x}{- 29} = \frac{- 29}{- 29}$

$y = - 3 + 4 x$

Divide $x$ by $1$ .

$x = \frac{- 29}{- 29}$

$y = - 3 + 4 x$

$x = \frac{- 29}{- 29}$

$y = - 3 + 4 x$

Divide $- 29$ by $- 29$ .

$x = 1$

$y = - 3 + 4 x$

$x = 1$

$y = - 3 + 4 x$

$x = 1$

$y = - 3 + 4 x$

Replace all occurrences of $x$ with $1$ in each equation.

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Replace all occurrences of $x$ in $y = - 3 + 4 x$ with $1$ .

$y = - 3 + 4 (1)$

$x = 1$

Simplify $- 3 + 4 (1)$ .

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Multiply $4$ by $1$ .

$y = - 3 + 4$

$x = 1$

Add $- 3$ and $4$ .

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 1)$

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Solve by Substitution 4x-y=3 , 7x-9y=-2

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